The story
Uitbuiken is Dutch, informal, and very specific. It is built from uit, out, and buik, belly, and it means sitting back after a big meal, or between courses, and giving the stomach a chance to catch up. There is a second, rarer use as well: a gentle walk after dinner, for which there is also the word uitbuikwandeling.
The word is used without embarrassment. At a Dutch dinner someone may push their chair back, loosen a belt and announce that they need to uitbuiken before dessert, and nobody thinks it rude. It names a pause the whole table is taking anyway.
There is an older, unrelated uitbuiken, from the verb buiken, to bulge. In the 17th century the writer P.C. Hooft used it for the river Meuse bulging out at a bend, and engineers later used it for a plate pushed outwards by steam pressure. That sense has died out, although anyone who has eaten too much may see the joke.
English has phrases for the moment, such as letting it go down or letting it settle, and plenty of people loosen a belt at Christmas. What it lacks is a verb that makes the pause sound like an activity. In Dutch you are not simply too full to move. You are busy: you are uitbuiken.
It is a word for the middle of the evening, after the main course and before the coffee, when the conversation slows and nobody is in a hurry.